There is a debate about the ontological status of mathematical objects, e.g. are they real or fictitious.
Your pluralist position is ambiguous from that perspective. For example, you could say that the entire multiverse of math is fictional, or you could say there’s only one actual world of math but we don’t/can’t know what it is so we need pluralism methodologically, or you could even be a multiverse-of-math Platonic realist and say e.g. that all the different models of set theory correspond to distinct and completely real Platonic realms. (This last may be the position of @Joel David Hamkins, who made his first post here a week ago, though I’m not sure.)
Do you favor a particular ontological interpretation of pluralism?
I think Benacerraf’s epistemological argument just is a knockdown against almost any form of platonism to me. You don’t have to agree because I think at this level of metaphysics there’s a lot of intuitions dominating, but for me it makes platonism entirely implausible. I’m not too decided on ontological status right now, maybe I’m some sort of eliminative structuralist or something? But I could be moved. Obviously when I do maths I act as though I’m a platonist and when I talk about morality I act as though I’m a realist, but in both cases I am not.
But yes, I think probably most of the debates between e.g. Woodin, Hamkins, etc about pluralism/non-pluralism are for the most part better thought of as methodological debates with a philosophical undercurrent.
There is a debate about the ontological status of mathematical objects, e.g. are they real or fictitious.
Your pluralist position is ambiguous from that perspective. For example, you could say that the entire multiverse of math is fictional, or you could say there’s only one actual world of math but we don’t/can’t know what it is so we need pluralism methodologically, or you could even be a multiverse-of-math Platonic realist and say e.g. that all the different models of set theory correspond to distinct and completely real Platonic realms. (This last may be the position of @Joel David Hamkins, who made his first post here a week ago, though I’m not sure.)
Do you favor a particular ontological interpretation of pluralism?
I think Benacerraf’s epistemological argument just is a knockdown against almost any form of platonism to me. You don’t have to agree because I think at this level of metaphysics there’s a lot of intuitions dominating, but for me it makes platonism entirely implausible. I’m not too decided on ontological status right now, maybe I’m some sort of eliminative structuralist or something? But I could be moved. Obviously when I do maths I act as though I’m a platonist and when I talk about morality I act as though I’m a realist, but in both cases I am not.
But yes, I think probably most of the debates between e.g. Woodin, Hamkins, etc about pluralism/non-pluralism are for the most part better thought of as methodological debates with a philosophical undercurrent.